I can understand how someone could be OK with dinghy sailing but not a bigger boat. When you capsize a 420 or a Laser, you swim around the other side and right the boat. You can't do that with a big boat. Hence - the fear. I actually still have that fear when I sail, but I thrive on the adrenaline rush and "perceived" danger. I guess the answer is - the boat, if it is knocked down and depending on the design - can take water in and there is always the potential for sinking.
A few notes on this though. First of all, my wife was terrified when we first started going out. I spent a lot of time showing her how reefing reduces speed and heel. I showed her how to play the main sheet in gusts. I showed her how turning up and "pinching" when hard over can stall your sails. Toward the end of the season, I had her on the tiller and I was walking her through doing all of these things (as opposed to me on the tiller showing her). This went a long way to making her feel better. On our new Passport 40, the main sheet is by the companionway - well away from the wheel. I'm a bit nervous myself - I'm used to being able to control it. I may see how I can reroute it so I can access it from the wheel.
Another couple of notes - Generally speaking, a broach or knockdown in a keel boat will happen fairly slowly (relative to a small boat). You'll know what's going on. Can you change it? Only if you move quickly to dump the main or other sails, and even then it may be difficult. But you get time to mentally prepare for it. More often than not, unless you have your chute out, the boat will heavily round up before you have a complete knockdown. Except on pure racing boats with exceptionally deep rudders, the rudder will come out of the water and the boat will "quickly" turn into the wind, usually righting itself in the process. A chute may keep it pinned down. Also, the closer the mast gets to the water, the quicker the sails will stall, the slower the boat will go, the slower the water will move over the rudder and the natural tendency of the boat wanting to head into the wind will take over.
Of course, you also have to be smart about the weather you're in relative to the boat you're sailing. A light displacement large sail plan boat is going to have many more problems sooner than a heavy displacement medium sail plan boat. Also, "bluewater cruisers" (see threads in "buying a boat") are designed to have a lot less risk of taking on water due to knockdown than a coastal cruiser.
Here's a Melges racer broaching (right at the start of the video) and recovering... http://www.youtube.com/watch?v=O0oOaF-_TjM